1 Stats 1.1.2 , 1.1.3 , 1.1.4

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Objective(s):

After this class, student should be able to:

1.1.2 Calculate the mean and standard deviation of a set of values
1.1.3 State that the term standard deviation is used to summarize the spread of values around the mean and that 68% of the values fall within one standard deviation of the mean
1.1.4 Explain how standard deviation is useful for comparing the means and the spread of data between two or more samples

Lesson: Standard Deviation

  • Review purpose of different graphs: pie, bar, histogram, scatterplot, line
  • Use IA guide (Talbot, p54...) to make sure students complete their brought-to-class graph with all IB required elements of a graph

What is "standard deviation? (SD)"
  • introduce "normal distribution" and the bell curve; explain its significance
  • Identify the "mean" in a bell curve
  • relate SD to the bell curve
  • explain how "1 SD" can be a variety of values like "2.0 cm" or "850 cc"
  • show that 1 SD on a normal distribution will encompass 68 % of all the measurements (see textbook, p. 5)

Use calculator to find standard deviation (SD).
  • For Ti-84 instructions on "how to..." visit MathBits.com.
  • To see what standard deviation is visit Wikipedia.org or easycalculation.com.
    Note: According to Merson-Davies, (2005, p 15), "record the SD to two significant figures and do not have more than the same number of decimal places for the mean."
  • With determining SD, students do NOT have to know the equation for SD, but students DO HAVE TO be able to use their calculator to find mean and SD. Note that it is a LOT easier in a spreadsheet, but this is useful only for writing labs; not in tests :(
  • Like Plato once said, "Know thy calculator!"

Complete the following table:
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 Height / cm +/- 0.5 cm
 Maximum lung capacity / L +/- 0.02 L
Group
 range (min - max)
 mean
 standard deviation
 range (min - max)
 mean
 standard deviation
I
 153 - 159
 156.6
 2.0


II





III





IV






Graph the results:
  • Use the processed data in the table above to make a graph.
    • Your graph will have only four points (each of them a mean)
    • Also add the "error" bars - use SD this time instead of range and "error"
  • Make graph according to all the IB graph requirements